Exercise

$p$ and $q$ are the zeroes of a polynomial $2x^2+5x-4$. Without finding the actual values of $p$ and $q$, evaluate $\left(1-p\right)\left(1-q\right)$. Show your steps.

Write a quadratic polynomial whose sum of zeroes is less than that of polynomial 

Shown below is a part of the graph of a polynomial $h\left(x\right)$

On dividing $h\left(x\right)$ by which of the following, the remainder will be zero?

$\left(\mathrm{i}\right) \left(x-2\right)$

$\left(\mathrm{ii}\right) \left(x+2\right)$

$\left(\mathrm{iii}\right) \left(x-4\right)$

$\left(\mathrm{iv}\right) \left(x+4\right)$

Shown below are the parts of graphs of two polynomials, $g\left(x\right)$ and $h\left(x\right)$. When $h\left(x\right)$ is divided by $\left(x-3\right)$, the remainder is $k$

Which of these is true for the remainder when $g\left(x\right)$ is divided by $\left(x-3\right)$?

If $a(70a-12b+2c)>0$ and the quadratic equation $a{x}^2+bx+c=0$ real roots $\alpha$ and $\beta$, then which of the following statements is always false?

The graph of a polynomial $p\left(x\right)$ passes through the points $(-5, 0), (0,-40), (8, 0)$ and $(5,-30)$. Which among the following is a factor of $p\left(x\right)$?

If $\alpha$ and $\beta$ are the zeroes of the polynomial $a{x}^2+bx+c,$ then the value of $\frac{1}{\alpha }+\frac{1}{\beta }$ is,

A graph of a cubic polynomial is plotted on a graph paper.

What is the sum of the roots of the polynomial?